Suppose the letters $a, \,b, \,c, \,d, \,e, \,f$ have probabilities $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \frac{1}{32}$, respectively.
Which of the following is the Huffman code for the letter $a, \,b, \,c, \,d, \,e, \,f$?
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$0$, $10$, $110$, $1110$, $11110$, $11111$
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$11$, $10$, $011$, $010$, $001$, $000$
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$11$, $10$, $01$, $001$, $0001$, $0000$
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$110$, $100$, $010$, $000$, $001$, $111$